Perfect Elimination Orderings for Symmetric Matrices

Monique Laurent; Shin-ichi Tanigawa

Perfect Elimination Orderings for Symmetric Matrices

Monique Laurent
, Shin-ichi Tanigawa

Research output: Working paper › Other research output

Abstract

We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of monotone families of chordal graphs, Robinsonian matrices and ultrametrics. We give a structural characterization for matrices that admit perfect elimination orderings in terms of forbidden substructures generalizing chordless cycles in graphs.

Original language	English
Place of Publication	Ithaca
Publisher	Cornell University Library
Number of pages	17
Publication status	Published - 17 Apr 2017

Publication series

Name	arXiv
Volume	1706.05115

Keywords

Chordal graph
Perfect elimination ordering
Unit interval
Ultrametric
Shortest path metric
Robinson matrix

Access to Document

http://arxiv.org/pdf/1704.05115.pdf

Perfect elimination orderings for symmetric matrices
Laurent, M. & Tanigawa, S.-I., Mar 2020, In: Optimization Letters. 14, 2, p. 339-353
Research output: Contribution to journal › Article › Scientific › peer-review

Open Access
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Cite this

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AB - We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of monotone families of chordal graphs, Robinsonian matrices and ultrametrics. We give a structural characterization for matrices that admit perfect elimination orderings in terms of forbidden substructures generalizing chordless cycles in graphs.

KW - Chordal graph

KW - Perfect elimination ordering

KW - Unit interval

KW - Ultrametric

KW - Shortest path metric

KW - Robinson matrix

M3 - Working paper

T3 - arXiv

BT - Perfect Elimination Orderings for Symmetric Matrices

PB - Cornell University Library

CY - Ithaca

ER -

Perfect Elimination Orderings for Symmetric Matrices

Abstract

Publication series

Keywords

Access to Document

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Research output

Perfect elimination orderings for symmetric matrices

Cite this